Consider the following four schedules due to three transactions (indicated by…

20172014

Consider the following four schedules due to three transactions (indicated by the subscript) using read and write on a data item X, denoted by r(X) and w(X) respectively. Which one of them is conflict serializable ?

S1 : r1 (X); r2 (X); w1 (X); r3 (X); w2 (X)

S2 : r2 (X); r1 (X); w2 (X); r3 (X); w1 (X)

S3 : r3 (X); r2 (X); r1 (X); w2 (X); w1 (X)

S4 : r2 (X); w2 (X); r3 (X); r1 (X); w1 (X)

  1. A.

    S1

  2. B.

    S2

  3. C.

    S3

  4. D.

    S4

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Correct answer: D

Answer: Schedule S4 is conflict serializable. It is equivalent to the serial order T2, T3, T1.

Reason (precedence graph):

  • w2(X) occurs before r3(X), so there is an edge from T2 to T3.

  • w2(X) occurs before r1(X) and before w1(X), so there is an edge from T2 to T1.

  • r3(X) occurs before w1(X), so there is an edge from T3 to T1.

The resulting precedence graph has edges T2 -> T3, T2 -> T1, and T3 -> T1. There are no edges pointing back to T2 or T3, so the graph is acyclic. A topological ordering is T2, T3, T1, which gives the equivalent serial schedule.

Why the other schedules fail:

  • S1 and S2 produce mutual conflicts between T1 and T2 (edges in both directions), creating a cycle.

  • S3 also produces a cycle between T1 and T2 via their read/write ordering, so it is not conflict serializable.

Conclusion: Only S4 is conflict serializable, equivalent to the serial execution T2; T3; T1.

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